Multivariate S-procedure

Different variants of the S-procedure provides a very important tool in robust stability and robust performance analysis. Concerning performance assessment this paper shows that the design framework based on the full block S-procedure (extended KYP lemma) contains an inherent conservativeness. The main result of the paper is a multivariate version of the classical S-procedure, stated for negative graph subspaces. A new solvability condition for the Elimination lemma is also provided.